For economic benefits and efficient management of resources, organizations are increasingly moving towards the paradigm of “cloud computing” by which they are allowed on-demand delivery of hardware, software and data as services. However, there are many security challenges which are particularly exacerbated by the multitenancy and virtualization features of cloud computing that allow sharing of resources among potentially untrusted tenants in access controlled cloud data centers. This can result in increased risk of data leakage. To address this risk vulnerability, we propose an efficient risk-aware virtual resource assignment mechanism for clouds multitenant environment. In particular, we introduce the notion of sensitivity in data centers and the objective is to minimize the risk of data leakage. In addition, the risk should not exceed in high sensitivity data centers in comparison to low sensitivity data centers. We present three assignment heuristics and compare their relative performance.